app.js

// you probably want to keep track of the backgrounding state of the app to respond differently

var backgrounded = false;
Ti.App.addEventListener('pause', function() {
  backgrounded = true;
});
Ti.App.addEventListener('resume', function() {
  backgrounded = false;
});
Ti.App.addEventListener('resumed', function() {
  backgrounded = false;
});

geolocation.js

// start monitoring a region
Ti.Geolocation.startMonitoring({
  lat: 123.33,
  lng: 45.34,
  accuracy: 5,
  radius: 100,
  identifier: "the region identifier"
});

// react when a region is entered
Ti.Geolocation.addEventListener('enteredRegion', function(e) {
  if (backgrounded) {
    // use a local notification
  } else {
    var alertDialog = Titanium.UI.createAlertDialog({
      title: 'Geofencing',
      message: "You entered the region identified by " + e.region.identifier
    });
    alertDialog.show();
  }
});

// react when a region is exited
Ti.Geolocation.addEventListener('exitedRegion', function(e) {
  if (backgrounded) {
    // use a local notification
  } else {
    var alertDialog = Titanium.UI.createAlertDialog({
      title: 'Geofencing',
      message: "You exited the region identified by " + e.region.identifier
    });
    alertDialog.show();
  }
});

// stop monitoring a region
Ti.Geolocation.stopMonitoring({
  lat: 123.33,
  lng: 45.34,
  accuracy: 5,
  radius: 100,
  identifier: "the region identifier"
});

// get an array of monitored regions - each region is a hash of lat, lng, accuracy, radius, identifier
regions = Ti.Geolocation.monitoredRegions();

GeolocationModule.mm

// this file located in /Library/Application Support/Titanium/mobilesdk/osx/{version_number}
// add the following methods to GeolocationModule.mm

- (void)locationManager:(CLLocationManager *)manager didEnterRegion:(CLRegion *)region
{
    NSDictionary *event = [NSDictionary dictionaryWithObjectsAndKeys:NUMBOOL(YES),@"success",[NSDictionary dictionaryWithObjectsAndKeys:NUMDOUBLE(region.center.latitude),@"lat",NUMDOUBLE(region.center.longitude),@"lng",NUMDOUBLE(region.radius),@"radius",region.identifier,@"identifier",nil],@"region",nil];

    if ([self _hasListeners:@"enteredRegion"])
    {
        [self fireEvent:@"enteredRegion" withObject:event];
    }
}

- (void)locationManager:(CLLocationManager *)manager didExitRegion:(CLRegion *)region
{
    NSDictionary *event = [NSDictionary dictionaryWithObjectsAndKeys:NUMBOOL(YES),@"success",[NSDictionary dictionaryWithObjectsAndKeys:NUMDOUBLE(region.center.latitude),@"lat",NUMDOUBLE(region.center.longitude),@"lng",NUMDOUBLE(region.radius),@"radius",region.identifier,@"identifier",nil],@"region",nil];
    
	if ([self _hasListeners:@"exitedRegion"])
    {
        [self fireEvent:@"exitedRegion" withObject:event];
    }
}

-(void)startMonitoring:(id)args
{
    ENSURE_UI_THREAD(startMonitoring,args);
    ENSURE_SINGLE_ARG(args,NSDictionary);
    
    CGFloat lat = [TiUtils floatValue:[args objectForKey:@"lat"]];
    CGFloat lng = [TiUtils floatValue:[args objectForKey:@"lng"]];
    CGFloat accuracy = [TiUtils floatValue:[args objectForKey:@"accuracy"]];
    CGFloat radius = [TiUtils floatValue:[args objectForKey:@"radius"]];
    NSString *identifier = [TiUtils stringValue:[args objectForKey:@"identifier"]];
    
    CLLocationManager *lm = [self locationManager];
    
    if ([CLLocationManager regionMonitoringAvailable] && [CLLocationManager regionMonitoringEnabled]) {
        CLLocationCoordinate2D location;
        location.latitude=lat;
        location.longitude=lng;
        CLLocationDistance regionRadius = radius;
        CLRegion *grRegion = [[CLRegion alloc] initCircularRegionWithCenter:location radius:regionRadius identifier:identifier];
        if ([lm respondsToSelector:(@selector(startMonitoringForRegion:desiredAccuracy:))]) {
            [lm startMonitoringForRegion:grRegion desiredAccuracy:accuracy];
        }
    }
}

-(void)stopMonitoring:(id)args
{
    ENSURE_UI_THREAD(stopMonitoring,args);
    ENSURE_SINGLE_ARG(args,NSDictionary);
    
    CGFloat lat = [TiUtils floatValue:[args objectForKey:@"lat"]];
    CGFloat lng = [TiUtils floatValue:[args objectForKey:@"lng"]];
    CGFloat radius = [TiUtils floatValue:[args objectForKey:@"radius"]];
    NSString *identifier = [TiUtils stringValue:[args objectForKey:@"identifier"]];
    
    CLLocationManager *lm = [self locationManager];
    
    if ([CLLocationManager regionMonitoringAvailable] && [CLLocationManager regionMonitoringEnabled]) {
        CLLocationCoordinate2D location;
        location.latitude=lat;
        location.longitude=lng;
        CLLocationDistance regionRadius = radius;
        CLRegion *grRegion = [[CLRegion alloc] initCircularRegionWithCenter:location radius:regionRadius identifier:identifier];
        if ([lm respondsToSelector:(@selector(stopMonitoringForRegion:))]) {
            [lm stopMonitoringForRegion:grRegion];
        }
    }
}

-(id)monitoredRegions:(id)args
{
    CLLocationManager *lm = [self locationManager];
    NSArray *allRegions = [[lm monitoredRegions] allObjects];
    NSMutableArray *regionDictionaryArray = [[NSMutableArray alloc] init];
    for (id region in allRegions) {
        NSDictionary *jsonRegion = [NSDictionary dictionaryWithObjectsAndKeys:NUMDOUBLE(((CLRegion *)region).center.latitude),@"lat",NUMDOUBLE(((CLRegion *)region).center.longitude),@"lng",NUMDOUBLE(((CLRegion *)region).radius),@"radius",((CLRegion *)region).identifier,@"identifier",nil];
        
        [regionDictionaryArray addObject:jsonRegion];
    }
    return regionDictionaryArray;
}